Simplify 3 cube root of 56y^6z^3

$3 \sqrt[3]{56 y^{6} z^{3}}$

Step 1

Rewrite $56 y^{6} z^{3}$ as ${(2 y^{2} z)}^{3} \cdot 7$ .

Factor $8$ out of $56$ .

$3 \sqrt[3]{8 (7) y^{6} z^{3}}$

Rewrite $8$ as $2^{3}$ .

$3 \sqrt[3]{2^{3} \cdot 7 y^{6} z^{3}}$

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

$3 \sqrt[3]{2^{3} \cdot 7 {(y^{2})}^{3} z^{3}}$

Move $7$ .

$3 \sqrt[3]{2^{3} {(y^{2})}^{3} z^{3} \cdot 7}$

Rewrite $2^{3} {(y^{2})}^{3} z^{3}$ as ${(2 y^{2} z)}^{3}$ .

$3 \sqrt[3]{{(2 y^{2} z)}^{3} \cdot 7}$

Step 2

Pull terms out from under the radical.

$3 (2 y^{2} z \sqrt[3]{7})$

Step 3

Multiply $2$ by $3$ .

$6 y^{2} z \sqrt[3]{7}$